To consider the probability of the slow-roll inflation in the modified LQC models, let us start with the phase space \(\mathbb {S}\)  of the modified Friedmann and Klein-Gordon equations,
which now is four-dimensional (4D), and consists of the four variables, \((v, \; b)\)  and \((\phi , \; p_\phi )\) , from the gravitational and matter sectors, respectively.
Using the canonical commutation relations, the symplectic form on the 4D phase space is given by [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]},
\(\Omega =d p_\phi \wedge d\phi + \frac{d v \wedge d b}{4 \pi G \gamma }.\) 
